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Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
TitleTitle
Georg Raffelt, Max-Planck-Institut für Physik, Georg Raffelt, Max-Planck-Institut für Physik, MünchenMünchen
36th CAST Collaboration Meeting, 29-30 May 2008, Paris36th CAST Collaboration Meeting, 29-30 May 2008, Paris
Update and interpretation of theUpdate and interpretation of theaxion hot dark matter limitaxion hot dark matter limit
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
MotivationMotivation
Observations of the mass-density distribution in the universeObservations of the mass-density distribution in the universeprovides very restrictive limits on a possible hot dark matterprovides very restrictive limits on a possible hot dark mattercomponent component
Restrictive limits exist on neutrino masses (in the sub-eV range) Restrictive limits exist on neutrino masses (in the sub-eV range)
Analogous arguments for hypothetical particles (e.g. axions)Analogous arguments for hypothetical particles (e.g. axions)In principle relevant for CAST search (sub-eV to eV range)In principle relevant for CAST search (sub-eV to eV range)
What are the particle-physics assumptions entering such limits?What are the particle-physics assumptions entering such limits?
How reliable are the cosmological limits?How reliable are the cosmological limits?
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
Limits from CAST-I and CAST-IILimits from CAST-I and CAST-II
CAST-I results: PRL 94:121301 (2005) and JCAP 0704 (2007) 010 CAST-I results: PRL 94:121301 (2005) and JCAP 0704 (2007) 010 CAST-II results (He-4 filling): preliminaryCAST-II results (He-4 filling): preliminary
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
SDSS SurveySDSS Survey
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
Structure Formation in the UniverseStructure Formation in the Universe
SmoothSmooth StructuredStructured
Structure forms byStructure forms by gravitational instabilitygravitational instability of primordialof primordial density fluctuationsdensity fluctuations
A fraction of hot dark matter A fraction of hot dark matter suppresses small-scale structuresuppresses small-scale structure
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
What is wrong with neutrino dark matter?What is wrong with neutrino dark matter?
Galactic Phase Space (“Tremaine-Gunn-Limit”)Galactic Phase Space (“Tremaine-Gunn-Limit”)
mm >> 20 20 40 eV 40 eV
2
3escape
n
2
3max
max3
)vm(m
3
pm
max
2
3escape
n
2
3max
max3
)vm(m
3
pm
max
Maximum mass density of a degenerateMaximum mass density of a degenerateFermi gasFermi gas
mm >> 100 100 200 eV 200 eV
SpiralSpiral galaxiesgalaxies
DwarfDwarf galaxiesgalaxies
• Nus are “Hot Dark Matter”Nus are “Hot Dark Matter”• Ruled out Ruled out by structure formationby structure formation
Neutrino Free Streaming (Collisionless Phase Mixing)Neutrino Free Streaming (Collisionless Phase Mixing)
• AtAt TT << 11 MeVMeV neutrinoneutrino scatteringscattering inin earlyearly universeuniverse ineffectiveineffective• Stream freely until non-relativisticStream freely until non-relativistic• Wash out density contrasts on small scales Wash out density contrasts on small scales
NeutrinosNeutrinosNeutrinosNeutrinos
Over-densityOver-density
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
Structure Formation with Hot Dark MatterStructure Formation with Hot Dark Matter
Troels Haugbølle, http://whome.phys.au.dk/~haugboelTroels Haugbølle, http://whome.phys.au.dk/~haugboel
Neutrinos with Neutrinos with mm = 6.9 eV = 6.9 eVStandard Standard CDM ModelCDM Model
Structure fromation simulated with Gadget codeStructure fromation simulated with Gadget codeCube size 256 Mpc at zero redshiftCube size 256 Mpc at zero redshift
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
Power Spectrum of Density FluctuationsPower Spectrum of Density Fluctuations
Field of density fluctuationsField of density fluctuations
)x(
)x(
)x()x(
Fourier transformFourier transform
)x(exd xik3k )x(exd xik3k
Power spectrum essentially squarePower spectrum essentially squareof Fourier transformationof Fourier transformation
)k(Pkkˆ2 3kk )k(Pkkˆ2 3kk
Power spectrum is Fourier transform ofPower spectrum is Fourier transform oftwo-point correlation function (two-point correlation function (x=xx=x22xx11) )
)k(Pe
2
kd)x()x()x( xik
3
3
12
)k(Pe
2
kd)x()x()x( xik
3
3
12
)k(
2
3xik
2
2
)k(Pke
kdk
4d
)k(
2
3xik
2
2
)k(Pke
kdk
4d
with the with the -function-function
Gaussian random field (phases ofGaussian random field (phases ofFourier modes Fourier modes kk uncorrelated) is fully uncorrelated) is fully
characterized by the power spectrumcharacterized by the power spectrum2
k)k(P 2k)k(P
or equivalently byor equivalently by
2k
2
)k(Pk)k( k
2321
2
3
2k
2
)k(Pk)k( k
2321
2
3
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
Power Spectrum of Cosmic Density Power Spectrum of Cosmic Density FluctuationsFluctuations
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
Neutrino Free Streaming – Transfer FunctionNeutrino Free Streaming – Transfer Function
Hannestad, Neutrinos in Cosmology, hep-ph/0404239Hannestad, Neutrinos in Cosmology, hep-ph/0404239
Transfer functionTransfer function
P(k) = T(k) PP(k) = T(k) P00(k)(k)
Effect of neutrino freeEffect of neutrino freestreaming on small scalesstreaming on small scales
T(k) = 1 T(k) = 1 8 8//M M
valid forvalid for
88//M M ≪ ≪ 11
Power suppression for Power suppression for FSFS ≳ ≳ 100 Mpc/h100 Mpc/h
mm = 0 = 0
mm = 0.3 eV = 0.3 eV
mm = 1 eV = 1 eV
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
Lyman-alpha ForestLyman-alpha Forest
• Hydrogen clouds absorb from QSOHydrogen clouds absorb from QSO continuum emission spectrumcontinuum emission spectrum
• Absorption dips at Ly-Absorption dips at Ly- wavelengh wavelengh corresponding to redshiftcorresponding to redshift
www.astro.ucla.edu/~wright/Lyman-alpha-forest.htmlwww.astro.ucla.edu/~wright/Lyman-alpha-forest.html
Examples for Lyman-Examples for Lyman- forest in forest inlow- and high-redshift quasarslow- and high-redshift quasars
http://www.astr.ua.edu/keel/agn/forest.gifhttp://www.astr.ua.edu/keel/agn/forest.gif
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
Some Recent Cosmological Limits on Neutrino Some Recent Cosmological Limits on Neutrino MassesMassesmm/eV/eV(limit 95%CL)(limit 95%CL)
Data / PriorsData / Priors
Spergel et al. (WMAP) 2003Spergel et al. (WMAP) 2003 [astro-ph/0302209] [astro-ph/0302209] 0.690.69 WMAP-1, 2dF, HST, WMAP-1, 2dF, HST, 88
Hannestad 2003Hannestad 2003 [astro-ph/0303076][astro-ph/0303076]1.011.01 WMAP-1, CMB, 2dF, HSTWMAP-1, CMB, 2dF, HST
Crotty et al. 2004Crotty et al. 2004 [hep-ph/0402049][hep-ph/0402049]
1.01.00.60.6
WMAP-1, CMB, 2dF, SDSSWMAP-1, CMB, 2dF, SDSS& HST, SN& HST, SN
Hannestad 2004Hannestad 2004 [hep-ph/0409108][hep-ph/0409108] 0.650.65 WMAP-1, SDSS, SN Ia gold sample,WMAP-1, SDSS, SN Ia gold sample,
Ly-Ly- data from Keck sample data from Keck sample
Seljak et al. 2004Seljak et al. 2004 [[astro-ph/0407372]astro-ph/0407372]0.420.42 WMAP-1, SDSS, Bias,WMAP-1, SDSS, Bias,
Ly-Ly- data from SDSS sample data from SDSS sample
Spergel et al. 2006Spergel et al. 2006 [hep-ph/0409108][hep-ph/0409108] 0.680.68 WMAP-3, SDSS, 2dF, SN Ia, WMAP-3, SDSS, 2dF, SN Ia, 88
Seljak et al. 2006Seljak et al. 2006 [astro-ph/0604335][astro-ph/0604335]0.140.14 WMAP-3, CMB-small, SDSS, 2dF,WMAP-3, CMB-small, SDSS, 2dF,
SN Ia, BAO (SDSS), SN Ia, BAO (SDSS), Ly-Ly- (SDSS) (SDSS)
Hannestad et al. 2006Hannestad et al. 2006 [hep-ph/0409108][hep-ph/0409108] 0.300.30 WMAP-1, CMB-small, SDSS, 2dF,WMAP-1, CMB-small, SDSS, 2dF,
SN Ia, BAO (SDSS), SN Ia, BAO (SDSS), Ly-Ly- (SDSS) (SDSS)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
Weak Lensing Weak Lensing A Powerful Probe for the Future A Powerful Probe for the Future
UnlensedUnlensed LensedLensed
Distortion of background images by foreground matterDistortion of background images by foreground matter
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
Sensitivity Forecasts for Future LSS Sensitivity Forecasts for Future LSS ObservationsObservations
Kaplinghat, Knox & Song,Kaplinghat, Knox & Song,astro-ph/0303344astro-ph/0303344
σσ(m(mνν) ~ 0.15 eV ) ~ 0.15 eV (Planck)(Planck)
σσ(m(mνν) ~ 0.044 eV (CMBpol)) ~ 0.044 eV (CMBpol)CMB lensing CMB lensing
Lesgourgues, PastorLesgourgues, Pastor& Perotto,& Perotto,hep-ph/0403296 hep-ph/0403296
Planck & SDSS Planck & SDSS mm > 0.21 eV detectable > 0.21 eV detectable
at 2at 2
mm > 0.13 eV detectable > 0.13 eV detectable
at 2at 2Ideal CMB & 40 x SDSS Ideal CMB & 40 x SDSS
Abazajian & DodelsonAbazajian & Dodelsonastro-ph/0212216astro-ph/0212216
Future weak lensingFuture weak lensingsurvey 4000 degsurvey 4000 deg22
σσ(m(mνν) ~ 0.1 eV) ~ 0.1 eV
Wang, Haiman, Hu, Wang, Haiman, Hu, Khoury & May,Khoury & May,astro-ph/0505390astro-ph/0505390
Weak-lensing selectedWeak-lensing selectedsample of > 10sample of > 105 5 clustersclusters
σσ(m(mνν) ~ 0.03 eV) ~ 0.03 eV
Hannestad, Tu & WongHannestad, Tu & Wongastro-ph/0603019astro-ph/0603019
Weak-lensing tomographyWeak-lensing tomography(LSST plus Planck)(LSST plus Planck) σσ(m(mνν) ~ 0.05 eV) ~ 0.05 eV
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
Low-Mass Particle Densities in the UniverseLow-Mass Particle Densities in the Universe
PhotonsPhotons
NeutrinosNeutrinos
Axions (QCD)Axions (QCD)
ALPsALPs(two photon vertex)(two photon vertex)
410 cm410 cm33Cosmic microwave backgroundCosmic microwave backgroundradiation radiation T = 2.725 KT = 2.725 K
Freeze out at Freeze out at T ~ 2 MeVT ~ 2 MeVbefore ebefore eee annihilation annihilation
nn 113 nn 113
112 cm112 cm33 ( in one flavor)( in one flavor)
For fFor faa ~ 10 ~ 1077 GeV (m GeV (maa ~ 1 eV) ~ 1 eV)
Freeze out at Freeze out at T ~ 80 MeVT ~ 80 MeV((a interaction)a interaction)
~ 50 cm~ 50 cm33
Primakoff freeze outPrimakoff freeze out
(g(gaa ~ 10 ~ 101010 GeV GeV11))
T T ≫≫ T TQCDQCD ~ 200 MeV ~ 200 MeV< 10 cm< 10 cm33
• No useful hot dark matter limit on ALPs in the CAST search rangeNo useful hot dark matter limit on ALPs in the CAST search range (too few of them today if they couple only by two-photon vertex)(too few of them today if they couple only by two-photon vertex)
• Axion mass limit comparable to limit on Axion mass limit comparable to limit on mm
(Axion number density comparable to one neutrino flavor)(Axion number density comparable to one neutrino flavor)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
Axion Hot Dark Matter from Thermalization Axion Hot Dark Matter from Thermalization after after QCDQCD
Freeze-out temperatureFreeze-out temperature
Cosmic thermal degrees ofCosmic thermal degrees offreedom at axion freeze-outfreedom at axion freeze-out
Cosmic thermal degrees ofCosmic thermal degrees offreedom freedom
a)2
(ff
CL
0
00
a
aa
a)2
(ff
CL
0
00
a
aa
aa
Chang & Choi, PLB 316 (1993) 51Chang & Choi, PLB 316 (1993) 51Hannestad, Mirizzi & Raffelt, JCAP 07 (2005) 02Hannestad, Mirizzi & Raffelt, JCAP 07 (2005) 02
094.0)z1(3
z1Ca
094.0)z1(3
z1Ca
104 105 106 107
104 105 106 107
fa (GeV)
fa (GeV)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
Axion Hot Dark Matter Limits from Precision Axion Hot Dark Matter Limits from Precision DataData
mmaa < 1.0 eV (95% CL) < 1.0 eV (95% CL)
mmaa < 0.4 eV (95% CL) < 0.4 eV (95% CL)
WMAP-5, LSS, BAO, SNIaWMAP-5, LSS, BAO, SNIa
WMAP-3, small-scale CMB,WMAP-3, small-scale CMB,HST, BBN, LSS, HST, BBN, LSS, Ly-Ly-
Hannestad, Mirizzi, RaffeltHannestad, Mirizzi, Raffelt& Wong [arXiv:0803.1585]& Wong [arXiv:0803.1585]
Melchiorri, Mena & SlosarMelchiorri, Mena & Slosar[arXiv:0705.2695] [arXiv:0705.2695]
Marginalizing over unknown neutrino hot dark matter componentMarginalizing over unknown neutrino hot dark matter component
Credible regions for neutrino plus axion hotCredible regions for neutrino plus axion hotdark matter (WMAP-5, LSS, BAO, SNIa)dark matter (WMAP-5, LSS, BAO, SNIa)Hannestad, Mirizzi, Raffelt & WongHannestad, Mirizzi, Raffelt & Wong[arXiv:0803.1585][arXiv:0803.1585]
Dashed (red) curves: Same with WMAP-3Dashed (red) curves: Same with WMAP-3From HMRW [arXiv:0706.4198] From HMRW [arXiv:0706.4198]
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
Evolution of Axion Hot Dark Matter LimitsEvolution of Axion Hot Dark Matter Limits
mmaa < 1.0 eV (95% CL) < 1.0 eV (95% CL)
mmaa < 0.4 eV (95% CL) < 0.4 eV (95% CL)
WMAP-5WMAP-5, LSS, BAO, SNIa, LSS, BAO, SNIano Ly-no Ly-
mmmarginalizedmarginalized
WMAP-3WMAP-3, small-scale CMB,, small-scale CMB,HST, BBN, LSS, HST, BBN, LSS, Ly-Ly-
mmmarginalizedmarginalized
Hannestad, Mirizzi, RaffeltHannestad, Mirizzi, Raffelt& Wong [arXiv:0803.1585]& Wong [arXiv:0803.1585]
Melchiorri, Mena & SlosarMelchiorri, Mena & Slosar[arXiv:0705.2695] [arXiv:0705.2695]
mmaa < 1.05 eV (95% CL) < 1.05 eV (95% CL)
WMAP-1WMAP-1, LSS, HST, SNIa,, LSS, HST, SNIa,
Ly-Ly-mm
22 statisticsstatistics
Hannestad, Mirizzi & RaffeltHannestad, Mirizzi & Raffelt[hep-ph/0504059][hep-ph/0504059]
mmaa < 1.2 eV (95% CL) < 1.2 eV (95% CL)
WMAP-3WMAP-3, LSS, BAO, SNIa, LSS, BAO, SNIano Ly-no Ly-
mmmarginalizedmarginalized
Hannestad, Mirizzi, RaffeltHannestad, Mirizzi, Raffelt& Wong [arXiv:0706.4198]& Wong [arXiv:0706.4198]
• Including Ly-a together with WMAP-5 will likely worsen the limit of 0.4 eVIncluding Ly-a together with WMAP-5 will likely worsen the limit of 0.4 eV from WMAP-3 + Ly-from WMAP-3 + Ly-• Has not been done, but for neutrinos this is expectedHas not been done, but for neutrinos this is expected• WMAP-5 and Ly-WMAP-5 and Ly- more consistent with each other more consistent with each other• More consensus now that Ly-More consensus now that Ly- is dangerous is dangerous
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
ConclusionConclusion
For general ALPs (only two-photon coupling)For general ALPs (only two-photon coupling)no “competition” with CAST no “competition” with CAST
Most “aggressive” limits (using Ly-a) at ~ 0.4 eV (95Most “aggressive” limits (using Ly-a) at ~ 0.4 eV (95%% CL) CL)Probably large systematic uncertaintiesProbably large systematic uncertaintiesDO NOT STOP CAST NOW !!!DO NOT STOP CAST NOW !!!
Constraints can improve by better data (weak lensing)Constraints can improve by better data (weak lensing)Eventual detection of hot dark matter component ?Eventual detection of hot dark matter component ?(neutrinos guaranteed at ~ 0.05 eV)(neutrinos guaranteed at ~ 0.05 eV)
If neutrino masses are detected in the laboratory (0If neutrino masses are detected in the laboratory (022, KATRIN), KATRIN) Less room for axions in the hot dark matter inventoryLess room for axions in the hot dark matter inventory
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France
TitleTitleCAST search and cosmological limitsCAST search and cosmological limits
are nicely complementary!are nicely complementary!
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany CAST Collaboration Meeting, 29-30 May 2008, Paris, France